Let Y1, Y2, . . . , Yn be independent and identically
distributed with the following probability density function f(y) =
4(1 ? y) ^3, 0 < y < 1 //orf(y)= 0 otherwise

(a) Find the probability density function of Y(1) = min(Y1, . .
. , Yn).

(b) Find the probability that Y(1) is less than 0.1.

(c) Find the expected value of Y(1). (Hint: beta distribution).
(d) Find the variance of Y(1). (Hint: beta distribution).